The following references are cited in the specification. Disclosures of these references are incorporated herein by reference in their entirety.
List of References:
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With a single-wafer processing technology, cluster tools are widely used for wafer fabrication in semiconductor manufacturing. A typical cluster tool has several process modules (PMs), two loadlocks, and a wafer handling robot with a radical layout as shown in FIG. 1. Equipped with one or two arms for the robot, the corresponding tool is called a single or dual-arm cluster tool. Cassettes with lots of raw wafers are loaded into or unloaded from a cluster tool through the loadlocks. A wafer is unloaded from the loadlock by the robot and delivered to one or more PMs for processing in a pre-specified order decided by a recipe. Often, the wafers in a cassette have an identical recipe. A wafer should stay in a PM for a minimum time to be processed. After all operations are completed, it returns to the cassette from which it comes [Wu et al., 2010b]. When all the wafers in a cassette are processed, the cassette is unloaded from the loadlock such that another cassette can be loaded. In this way, with two loadlocks, a cluster tool can operate consecutively without interruption.
Cluster tools are a kind of robotic cells and a robotic cell is a flow-shop with blocking [Pinedo, 1995]. Extensive work has been done for the operation of a robotic cell [Brauner, 2008; Crama et al., 1997 and 2000; Dawande et al., 2002, 2007 and 2009; Geismar et al., 2006 and 2008; Sechi et al., 1992 and 2001]. They mainly focus on a flow-shop operation mode with one part type to be processed and a processed part can stay at a machine for an unlimited time. A cyclic schedule is called a k-unit schedule if exactly k parts are produced during every period [Sechi et al., 1992]. When k=1, it is a one-unit cyclic schedule. Owing to its easy implementation, one-unit cyclic schedule is the most desired in practice assuming that all the schedules achieve the same maximum throughput.
To effectively operate a single-cluster tool, plenty of studies have been done [Venkatesh et al., 1997; Perkinson et al., 1994 and 1996; Zuberek, 2001; Wu et al., 2011 and 2013; and Wu and Zhou, 2010a, 2012a, and 2012b]. They show that a cluster tool mostly operates under a steady state. If the robot is the bottleneck and the robot task time decides the cycle time of a tool, the tool operates in a transport-bound region. Contrarily, if the wafer processing time dominates the process and decides the cycle time, it operates in a process-bound region. In practice, the robot task time is much shorter than the wafer processing time [Lee et al., 2004; Lopez and Wood, 2003]. Thus, a single-arm cluster tool is mostly process-bound and a backward scheduling strategy is shown to be optimal [Lee et al., 2004; Lopez and Wood, 2003].
Some wafer fabrication processes impose strict wafer residency time constraints in a PM, which requires that a processed wafer be removed from the PM within a limited time, otherwise it suffers from serious quality problem [Kim et al., 2003; Lee and Park, 2005]. With such constraints, the scheduling problem of cluster tools becomes very complicated and challenging. Methods are developed in [Kim et al., 2003; Lee and Park, 2005] to schedule dual-arm cluster tools with wafer residency time constraints for cyclic scheduling. With Petri net models and robot waiting concept, much more efficient techniques are presented in [Wu et al., 2008; and Wu and Zhou, 2010a] for scheduling both single and dual-arm cluster tools.
In wafer fabrication, a wafer may need to visit some processing steps several times, leading to a revisiting process. Atomic layer deposition (ALD) is a typical revisiting process in the semiconductor manufacturing [Lee, et al., 2006]. With wafer revisiting, it is challenging to schedule a cluster tool. All the aforementioned studies are conducted on cluster tools for non-revisiting processes. To explore the potential in operating a cluster tool with wafer revisiting, methods are presented for performance evaluation by using Petri net models in [Zuberek, et al., 2004; and Wu and Zhou, 2010c] without providing a scheduling technique. Lee, et al. [2006] study the scheduling problem of single-arm cluster tools with wafer revisiting for the first time. In their work, based on a Petri net model, the problem is formulated as a mixed integer programming such that an optimal schedule can be found. This problem is further investigated in [Wu, et al., 2011] for the ALD process by using Petri net model and analytical expressions are derived to find the optimal schedule. For dual-arm cluster tools with wafer revisiting, based on a Petri net model, Wu et al., [2013a] find that, by using a swap strategy, the system may never enter a steady state and analytical expressions are presented to correctly calculate the cycle time. Based on this finding, effective methods are developed to schedule such dual-arm cluster tools in [Wu et al., 2013b; and Qiao et al., 2013].
With both wafer residency time constraints and revisiting, the scheduling problem of cluster tools is very complicated. Based on the scheduling strategy proposed in [Qiao et al., 2013], effective techniques are developed to schedule dual-arm cluster tools for the ALD process with wafer residency time constraints for different situations in [Qiao et al., 2014a and 2014b]. Up to now, there is no research report on scheduling single-cluster tools with both wafer residency time constraints and wafer revisiting. Notice that, with wafer revisiting, it is more difficult to balance the workloads among the steps for a single-arm cluster tool than for a dual-arm cluster tool, thereby, leading to a more difficult problem to schedule a single-arm tool than a dual-arm one.
There is a need in the art for a method to obtain a schedule when wafer revisiting process and residency time constraints are taken into consideration.